Apparatus and method for calibrating a camera

ABSTRACT

An apparatus for calibrating a camera comprises a camera; an input unit configured to receive a segmentation diagonal ratio of the environment quadrangle; a memory configured to store a program; and a processor configured to perform camera calibration based on the program, wherein the program is configured to: extract diagonal parameters of a centered quadrangle from the image; estimate length of a projection center line; estimate a projection angle; estimate an angle between diagonals of a projection quadrangle; estimate a projection center point; and estimate extrinsic and intrinsic parameters of the camera.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of Korean Patent Application No.10-2015-0016994, filed on Feb. 3, 2015, entitled “Apparatus and methodfor calibrating a camera”, which is hereby incorporated by reference inits entirety into this application.

BACKGROUND OF THE INVENTION

1. Technical Field

Exemplary embodiments of the present invention relate to a cameracalibration technology and more particularly, to a calibrationtechnology which estimates intrinsic and extrinsic parameters of acamera.

2. Description of the Related Art

A camera calibration is defined as to find out an intrinsic construction(for example, lens properties and imaging methods) and an extrinsicconstruction (for example, position and direction of a camera). It is amajor technical issue in a field of computer vision. It is also a coreelement technology in fields of geometric camera, robot navigation, 3Dreconstruction, and augmented reality whose interest has been increasedrecently.

Information on a camera intrinsic construction is not explicitly knownif not an expensive one, and it is not easy to measure information on acamera extrinsic construction except a special case. Accordingly, avariety of methods to measure such intrinsic and extrinsic constructioninformation are suggested, which usually use a singular image forthree-dimensional object constructed precisely in advance or a pluralityof images for a checkerboard whose size is known.

However, the three-dimensional object is so complicated that it is noteasy to use it in a normal environment and that it is not proper toapply to a cheap camera such as a smart phone camera. While a method touse a plurality of images for a simple checkerboard is most widely used,such a method takes a long time comparatively to measure so that it isnot easy to apply to a real time application.

SUMMARY OF THE INVENTION

In view of the above, the present invention provides an apparatus and amethod for calibrating a camera which is able to perform cameracalibration using a singular image including a quadrangle.

According to an aspect of the present invention, there is provided anapparatus for calibrating a camera comprising: a camera configured togenerate an image by photographing an environment quadrangle; an inputunit configured to receive a segmentation diagonal ratio of theenvironment quadrangle; a memory configured to store a program forcamera calibration; and a processor configured to perform cameracalibration based on the program, wherein the program is configured to:extract diagonal parameters of a centered quadrangle from the image;estimate length of a projection center line based on the segmentationdiagonal ratio of the environment quadrangle and the diagonal parametersof the centered quadrangle; estimate a projection angle corresponding toeach diagonal of the centered quadrangle based on the length of theprojection center line; estimate an angle between diagonals of aprojection quadrangle based on the projection angle and an angle betweendiagonals of the centered quadrangle; estimate a projection center pointbased on the projection angle, the angle between diagonals of thecentered quadrangle and the angle between diagonals of the projectionquadrangle; and estimate extrinsic and intrinsic parameters of thecamera corresponding to the projection center point and the centeredquadrangle.

The diagonal parameter may comprise the angle between diagonals of thecentered quadrangle and the segmentation diagonal ratio.

The projection angle may be an angle between the projection center lineand the diagonal of the environment quadrangle.

The program may be configured to: estimate a homography between thecentered quadrangle and the projection quadrangle; and recover theenvironment quadrangle by applying the homography to the imagequadrangle.

The program may be configured to estimate length of the projectioncenter line by the following Equation:

$d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}$where  A_(p, 0) = m₀²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²and  A_(p, 1) = m₀²α_(p, 0)²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²α_(p, 1)².

wherein the is m₀ is a segmentation diagonal ratio to one diagonal ofthe projection quadrangle, the m₁ is a segmentation diagonal ratio tothe other diagonal of the projection quadrangle, β is a value obtainedby dividing the segmentation diagonal ratio to one diagonal of thecentered quadrangle by the segmentation diagonal ratio to the otherdiagonal of the centered quadrangle.

The program may be configured to estimate the projection angle by thefollowing Equation:

${\cos\;\theta_{i}} = {{\frac{{m_{i + 2}l_{i}} - {m_{i}l_{i + 2}}}{m_{i}{m_{i + 2}\left( {l_{i} + l_{i + 2}} \right)}}d} = {\alpha_{p,i}d}}$

wherein the m_(i) is a segmentation diagonal ratio to one diagonal ofthe projection quadrangle, the m_(i+2) is a segmentation diagonal ratioto the other diagonal of the projection quadrangle, the l_(i) is asegmentation diagonal ratio to one diagonal of the centered quadrangle,the l_(i+2) is a segmentation diagonal ratio to the other diagonal ofthe centered quadrangle, d is length of the projection center line, theθ_(i) is a projection angle corresponding to each diagonal of thecentered quadrangle, the i is 0 or 1.

The program may be configured to estimate the angle between thediagonals by the following Equation:cos φ=cos ρ sin θ₀ sin θ₁+cos θ₀ sin θ₁

wherein the ρ is an angle between the diagonals of the centeredquadrangle, the φ is an angle between diagonals of the projectionquadrangle, the θ₀ is a projection angle corresponding to one diagonalof the centered quadrangle, θ₁ is a projection angle corresponding tothe other diagonal of the centered quadrangle.

The program may be configured to estimate the projection center point bythe following Equation:

$P_{c} = \frac{d\left( {{\sin\;\phi\;\cos\;\theta_{0}\cos\;\theta_{1}} - {\cos\;\phi\;\cos\;\theta_{0}\sin\;\rho\;\sin\;\theta_{0}\sin\;\theta_{1}}} \right)}{\sin\;\phi}$

wherein P_(c) is a projection center point, the ρ is an angle betweenthe diagonals of the centered quadrangle, the φ is an angle betweendiagonals of the projection quadrangle, the θ₀ is a projection anglecorresponding to one diagonal of the centered quadrangle, θ₁ is aprojection angle corresponding to the other diagonal of the centeredquadrangle, d is length of the projection center line.

According to another aspect of the present invention, there is provideda method for calibrating a camera comprising: receiving an image of anenvironment quadrangle and a segmentation diagonal ratio of theenvironment quadrangle;

extracting diagonal parameters of a centered quadrangle from the image;estimating length of a projection center line based on the segmentationdiagonal ratio of the environment quadrangle and the diagonal parametersof the centered quadrangle; estimating a projection angle correspondingto each diagonal of the centered quadrangle based on the length of theprojection center line; estimating an angle between diagonals of aprojection quadrangle based on the projection angle and an angle betweendiagonals of the centered quadrangle; estimating a projection centerpoint based on the projection angle, the angle between diagonals of thecentered quadrangle and the angle between diagonals of the projectionquadrangle; and estimating extrinsic and intrinsic parameters of thecamera corresponding to the projection center point and the centeredquadrangle.

The diagonal parameter may comprise the angle between diagonals of thecentered quadrangle and the segmentation diagonal ratio.

The projection angle may be an angle between the projection center lineand the diagonal of the environment quadrangle.

The method for calibrating a camera may further comprise estimating ahomography between the centered quadrangle and the projectionquadrangle; and recovering the environment quadrangle by applying thehomography to the image quadrangle.

The step for estimating length of a projection center line based on thesegmentation diagonal ratio of the environment quadrangle and thediagonal parameters of the centered quadrangle may comprise estimatinglength of a projection center line by the following Equation:

$d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}$where  A_(p, 0) = m₀²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²and  A_(p, 1) = m₀²α_(p, 0)²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²α_(p, 1)².

wherein the m₀ is a segmentation diagonal ratio to one diagonal of theprojection quadrangle, the m₁ is a segmentation diagonal ratio to theother diagonal of the projection quadrangle, β is a value obtained bydividing the segmentation diagonal ratio to one diagonal of the centeredquadrangle by the segmentation diagonal ratio to the other diagonal ofthe centered quadrangle.

The step for estimating a projection angle corresponding to eachdiagonal of the centered quadrangle based on the length of theprojection center line may comprise estimating a projection angle by thefollowing Equation:

${\cos\;\theta_{i}} = {{\frac{{m_{i + 2}l_{i}} - {m_{i}l_{i + 2}}}{m_{i}{m_{i + 2}\left( {l_{i} + l_{i + 2}} \right)}}d} = {\alpha_{p,i}d}}$

wherein the m_(i) is a segmentation diagonal ratio to one diagonal ofthe projection quadrangle, the m_(i+2) is a segmentation diagonal ratioto the other diagonal of the projection quadrangle, the l_(i) is asegmentation diagonal ratio to one diagonal of the centered quadrangle,the l_(i+2) is a segmentation diagonal ratio to the other diagonal ofthe centered quadrangle, d is length of the projection center line, theθ_(i) is a projection angle corresponding to each diagonal of thecentered quadrangle, the i is 0 or 1.

The step for estimating an angle between diagonals of a projectionquadrangle based on the projection angle and an angle between diagonalsof the centered quadrangle may comprise estimating an angle betweendiagonals by the following Equation:cos φ=cos ρ sin θ₀ sin θ₁+cos θ₀ sin θ₁

wherein the ρ is an angle between the diagonals of the centeredquadrangle, the φ is an angle between diagonals of the projectionquadrangle, the θ₀ is a projection angle corresponding to one diagonalof the centered quadrangle, θ₁ is a projection angle corresponding tothe other diagonal of the centered quadrangle.

The step for estimating a projection center point based on theprojection angle, the angle between diagonals of the centered quadrangleand the angle between diagonals of the projection quadrangle maycomprise estimating a projection center point by the following Equation:

$P_{c} = \frac{d\left( {{\sin\;\phi\;\cos\;\theta_{0}\cos\;\theta_{1}} - {\cos\;\phi\;\cos\;\theta_{0}\sin\;\rho\;\sin\;\theta_{0}\sin\;\theta_{1}}} \right)}{\sin\;\phi}$

wherein P_(c) is a projection center point, the ρ is an angle betweenthe diagonals of the centered quadrangle, the φ is an angle betweendiagonals of the projection quadrangle, the θ₀ is a projection anglecorresponding to one diagonal of the centered quadrangle, θ₁ is aprojection angle corresponding to the other diagonal of the centeredquadrangle, d is length of the projection center line.

As described above, according to an embodiment of the present invention,it allows camera calibration without using a complicated 3D object nor aplurality of images for a checkerboard.

According to an embodiment of the present invention, it also facilitatesto detect extrinsic parameters to express a projection center point andorientation.

According to an embodiment of the present invention, it further providescamera calibration of which calculation is not complicate and which isrobust to errors.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an apparatus for calibrating a camera according to anembodiment of the present invention.

FIG. 2 is a flowchart illustrating a method for calibrating a camerausing an apparatus for calibrating a camera according to an embodimentof the present invention.

FIG. 3 is a diagram to explain diagonal parameters which an apparatusfor calibrating a camera according to an embodiment of the presentinvention uses.

FIG. 4 is a schematic view illustrating a process for estimating acentered quadrangle by an apparatus for calibrating a camera accordingto an embodiment of the present invention.

FIG. 5 is a schematic view illustrating a process for estimating acentered quadrangle for an image quadrangle which is an isoscelestrapezoid by an apparatus for calibrating a camera according to anembodiment of the present invention.

FIG. 6 is a schematic view illustrating a process for estimating acentered quadrangle for an image quadrangle which is a parallelogram byan apparatus for calibrating a camera according to an embodiment of thepresent invention.

FIG. 7 illustrates a projection quadrangle estimated by an apparatus forcalibrating a camera according to an embodiment of the presentinvention.

FIG. 8 illustrates a case where a projection quadrangle is photographedby a first segment camera which an apparatus for calibrating a cameraaccording to an embodiment of the present invention assumes.

FIG. 9 illustrates a case where a projection quadrangle is photographedby a second segment camera which an apparatus for calibrating a cameraaccording to an embodiment of the present invention assumes.

FIG. 10 illustrates a case where a projection quadrangle is photographedby a first segment camera and a second segment camera which an apparatusfor calibrating a camera according to an embodiment of the presentinvention assumes.

FIG. 11 illustrates geometric relationship of a projection center line,a centered quadrangle and a projection quadrangle which are used by anapparatus for calibrating a camera according to an embodiment of thepresent invention.

FIG. 12 illustrates a centered quadrangle which an apparatus forcalibrating a camera according to an embodiment of the present inventionestimates.

FIG. 13 illustrates a case where an environment quadrangle isphotographed by a first segment camera which an apparatus forcalibrating a camera according to an embodiment of the present inventionassumes.

FIG. 14 illustrates a projection center point of a segment camera whichan apparatus for calibrating a camera according to an embodiment of thepresent invention assumes.

FIG. 15 illustrates geometric relationship between an environmentquadrangle and an image quadrangle which an apparatus for calibrating acamera according to an embodiment of the present invention inputs.

FIG. 16 illustrates a centered quadrangle which an apparatus forcalibrating a camera according to an embodiment of the present inventiongenerates.

FIG. 17 illustrates geometric relationship between an image quadrangleand an environment quadrangle which an apparatus for calibrating acamera according to an embodiment of the present invention inputs, acentered quadrangle and a projection quadrangle.

FIG. 18 is a plan view illustrating an environment quadrangle and aprojection quadrangle which an apparatus for calibrating a cameraaccording to an embodiment of the present invention estimates.

FIG. 19 illustrates the computer system implemented with the apparatusfor calibrating a camera in accordance with an embodiment of the presentinvention.

DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

The present invention will be described with reference to particularembodiments along with the accompanying drawings. However, it is to beappreciated that various changes and modifications may be made. Theexemplary embodiments disclosed in the present invention do not limitbut describe the spirit of the present invention, and the scope of thepresent invention is not limited by the exemplary embodiments. The scopeof the present invention should be interpreted that all spiritsequivalent to the following claims fall with the scope of the presentinvention.

The terms used in the description are intended to describe certainembodiments only, and shall by no means restrict the present invention.In the present description, when one element is described as“transmitting” a signal to another element, it shall be construed astransmitting to the other element directly but also as possibly havinganother element in between.

An apparatus for calibrating a camera according to an embodiment of thepresent invention recovers geometric information (diagonal angle, ratioof each segment length) of a quadrangle from a singular image of anarbitrary quadrangle of which shape information is not accurately known,recovers projection structure as a frustum based on the geometricinformation, calculates extrinsic parameters of a camera from thefrustum, and calculates intrinsic parameters.

FIG. 1 illustrates an apparatus for calibrating a camera according to anembodiment of the present invention.

Referring to FIG. 1, an apparatus for calibrating a camera may include aprocessor 110, a memory 120, a storage 130, an input unit 140 and acamera 150.

The processor 110 may perform functions for camera calibration accordingto programs loaded in the memory 120.

The memory 120 may store programs for camera calibration and transmits aprogram corresponding to a request from the processor 110 to theprocessor 110. Here, the memory 120 may be a volatile memory.

The storage 130 may be a storing medium to store programs for cameracalibration. The processor 110 may load the programs stored in thestorage 130 to the memory 120. The storage 130 may store an imageincluding an arbitrary quadrangle.

The input unit 140 may receive diagonal parameters of the originalquadrangle to store them in the storage 130 by being connected to aninput device (for example, an input device or an external input deviceinstalled in the apparatus for calibrating a camera).

The camera 150 may photograph an arbitrary environment quadrangle togenerate an image and store the image in the storage 130. Here, thecamera 150 may be a standard pin-hole model and focal distances of widthand length directions may be identical with each other. Here, anenvironment quadrangle may be a picture or an article having aquadrangle shape to be photographed for camera calibration.

Hereinafter, a process for performing camera calibration based on theprogram predetermined by an apparatus for calibrating a camera accordingto an embodiment of the present invention will be explained in detail.

FIG. 2 is a flowchart illustrating a method for calibrating a camerausing an apparatus for calibrating a camera according to an embodimentof the present invention. FIG. 3 is a diagram to explain diagonalparameters which an apparatus for calibrating a camera according to anembodiment of the present invention uses. General processes of loadingprograms to the memory 120 by the processor 110 and reading the programsloaded in the memory 120 by the processor 110, etc. will be omitted. Anobject will be called as an apparatus for calibrating a camera forsimplicity and clarity of the invention.

Referring to FIG. 2, in S210, an apparatus for calibrating a camera mayreceive an image including an arbitrary quadrangle, diagonal parametersof an environment quadrangle (hereinafter, a real quadrangle which is anobject of the image to be photographed is referred to as an environmentquadrangle) and an angle between diagonals of an environment quadrangle.Referring to FIG. 3, the diagonal parameter may include a length ratioand an angle (ρ) between two diagonals which connect vertexes of thequadrangle. The diagonal parameter may further include a ratio betweenthe distance from an intersection point of two diagonals (o) to one endpoint of the each diagonal and the distance from the intersection pointto another end point of the each diagonal (hereinafter, referred to as asegmentation diagonal ratio which corresponds to t₁, t₂ in Table 1). Forexample, when a diagonal length between a vertex v₁ and a vertex v₃ isnormalized as 1, t₁ is a length between the intersection point and thevertex v₁. When a diagonal length between a vertex v₂ and a vertex v₄ isnormalized as 1, t₂ is a length between the intersection point and thevertex v₂. For example, diagonal parameters may be represented by thefollowing Table 1 according to quadrangles.

TABLE 1 Diagonal parameters Category (l₂, t₁, t₂, ρ) Properties Square(1, 0.5, 0.5, π/2) Length of two diagonals is identical and thediagonals bisect each other, and meet at 90° Rectangle (1, 0.5, 0.5, ρ)Length of two diagonals is identical and the diagonals bisect each otherRhombus (l₂, 0.5, 0.5, π/2) The diagonals bisect each other and meet at90° Parallelogram (l₂, 0.5, 0.5, ρ) The diagonals bisect each other Kite(l₂, t₁, 0.5, π/2) or The diagonals meet at 90° and one (l₂, 0.5, t₂,π/2) diagonal is the perpendicular bisector of the other diagonalIsosceles (1, t₁, t₂, ρ) Length of two diagonals is identical trapezoidbut, t₁ = t₂ or t₁ + and the diagonals divide each other t₂ = 1. intosegments with lengths that are pairwise equal Trapezoid (l₂, t₁, t₂, ρ)The diagonals divide each other into but, t₁ = t₂ or t₁ + segments withlengths that are t₂ = 1. pairwise equal Quadrangle (l₂, t₁, t₂, ρ) Norestriction

In S220, the apparatus for calibrating a camera may extract a quadranglefrom the image. Hereinafter, the quadrangle extracted from the image iscalled as an image quadrangle. Here, the apparatus for calibrating acamera may describe the extracted image quadrangle with 4 vertexes.

In S230, the apparatus for calibrating a camera may estimate diagonalparameters corresponding to a centered quadrangle. Here, the centeredquadrangle is the quadrangle of which an intersection point of thediagonals is positioned at the center of the image. For example, theapparatus for calibrating a camera may detect a vanishing-line or twovanishing-points in the image, estimate the centered quadrangle from theimage quadrangle using the vanishing-line or vanishing-points andcalculate diagonal parameters of the centered quadrangle. A process forcalculating diagonal parameters corresponding to the centered quadrangleby the apparatus for calibrating a camera according to an embodiment ofthe present invention will be explained in more detail with reference toFIG. 4 to FIG. 6 later. Here, when the image quadrangle is apre-centered quadrangle, a process for estimating a centered quadrangleusing a vanishing-point method may be omitted.

In S240, the apparatus for calibrating a camera may estimate aprojection quadrangle using a segment camera pair. The apparatus forcalibrating a camera may estimate length of a projection center line anda diagonal angle of the projection quadrangle using the segment camerapair and then recover the projection quadrangle based on the length of aprojection center line, the diagonal angle of the projection quadrangle,and the diagonal parameter of the centered quadrangle. The projectioncenter line is a segment connecting between the projection center point,which is the position of each segment camera, and the intersection pointof two diagonals of the centered quadrangle. Here, the segment camera isa virtual camera which photographs a straight line in the environment. Aprocess for calculating a projection quadrangle using the segment camerapair by the apparatus for calibrating a camera will be explained in moredetail with reference to FIG. 7 to FIG. 14 later.

In S250, the apparatus for calibrating a camera may estimate a cameraposition (projection center point) based on a diagonal angle of thecentered quadrangle and the length of a projection center line. It willbe explained in more detail with reference to FIG. 7 to FIG. 14 later.

In S260, the apparatus for calibrating a camera may estimate anextrinsic parameter and an intrinsic parameter of the camera. Theintrinsic parameter of the camera 150 may be expressed as follows:

$K = \begin{bmatrix}f & 0 & {cx} \\0 & f & {cy} \\0 & 0 & 1\end{bmatrix}$

wherein, k is an intrinsic parameter, cx is a coordinate of the centerpoint of an image for the x-axis in a predetermined coordinate, and cyis a coordinate of the center point of an image for the y-axis in apredetermined coordinate. The apparatus for calibrating a camera maythus calculate the intrinsic parameter by estimating a size of the imagesince cx and cy are coordinates for the center point of the image andestimating f referring to the coordinate of the centered quadranglethrough a known method.

The apparatus for calibrating a camera may estimate translationaltransformation of the extrinsic parameter based on the projection centerpoint and estimate rotational transformation based on a homography ofthe projection quadrangle and the centered quadrangle. Here, theprojection quadrangle is a quadrangle expressed when the centeredquadrangle is projected to the projection plane which is parallel to theenvironment quadrangle based on the projection center point. Theapparatus for calibrating a camera may thus estimate extrinsicparameters including the projection center point, the translationaltransformation and the rotational transformation.

In S270, the apparatus for calibrating a camera estimate vertexpositions of the environment quadrangle by applying the homography tothe image quadrangle. Each vertex position of the environment quadranglemay be thus estimated by applying the homography representing therelationship between the centered quadrangle and the projectionquadrangle to the image quadrangle without processing vanishing-pointtransformation. A process for estimating extrinsic parameters using theprojection center point by the apparatus for calibrating a camera willbe explained in more detail with reference to FIG. 15 to FIG. 18 later.

The apparatus for calibrating a camera according to an embodiment of thepresent invention may perform camera calibration using the imagegenerated by the camera 150 and inputted diagonal parameters of theenvironment quadrangle.

FIG. 4 is a schematic view illustrating a process for estimating acentered quadrangle by an apparatus for calibrating a camera accordingto an embodiment of the present invention, FIG. 5 is a schematic viewillustrating a process for estimating a centered quadrangle for an imagequadrangle which is an isosceles trapezoid by an apparatus forcalibrating a camera according to an embodiment of the presentinvention, and FIG. 6 is a schematic view illustrating a process forestimating a centered quadrangle for an image quadrangle which is aparallelogram by an apparatus for calibrating a camera according to anembodiment of the present invention.

Referring to FIG. 4, the apparatus for calibrating a camera may detecttwo vanishing-points (W_(d,0), W_(d,1) of FIG. 4) of an image quadrangle410 using a known vanishing-point detection method. The apparatus forcalibrating a camera may also detect first extension intersection points(W_(1,0), W_(1,1) of FIG. 4) which are intersection points of extensionlines of each side of the image quadrangle and the segment connectingtwo vanishing-points. The apparatus for calibrating a camera may detectsecond extension intersection points (Us,₀, Us,₁ of FIG. 4) which areintersection points of the straight lines (hereinafter, referred to ascentered vanishing-line), connecting each vanishing-point and the centerpoint of the image, and the extension line of one side (side of U₀, U₁of FIG. 4) of the image quadrangle. The apparatus for calibrating acamera may further detect third extension intersection points (Us,₂,Us,₃ of FIG. 4) which are intersection points of the straight lines,connecting each of the first extension intersection point and each ofthe second extension intersection point, and the centeredvanishing-line. The apparatus for calibrating a camera may estimate acentered quadrangle 420 which is a quadrangle having vertexes of thesecond extension intersection points and the third extensionintersection points. Accordingly, the apparatus for calibrating a cameramay estimate diagonal parameters by obtaining four vertexes of thecentered quadrangle.

When the environment quadrangle is a quadrangle having a parallelcondition such as an isosceles trapezoid as shown in FIG. 5, theapparatus for calibrating a camera may detect one vanishing-point (forexample, W_(d,0) of FIG. 5) using a known vanishing-point detectionmethod and detect an intersection point of the extension lines of thesides, corresponding to two sides parallel to the environment quadrangleamong the sides of an image quadrangle 510, as the other vanishing-point(W₀ of FIG. 5). The apparatus for calibrating a camera may then estimatea centered quadrangle 520 using the detected two vanishing-points.

When the environment quadrangle is a parallelogram as shown in FIG. 6,the apparatus for calibrating a camera may detect each vanishing-point(W₀, W₁ of FIG. 6) which is each intersection point of extension linesof the sides of an image quadrangle corresponding to the parallel sidepair of the environment quadrangle.

FIG. 7 illustrates a projection quadrangle estimated by an apparatus forcalibrating a camera according to an embodiment of the presentinvention, FIG. 8 illustrates a case where a projection quadrangle isphotographed by a first segment camera which an apparatus forcalibrating a camera according to an embodiment of the present inventionassumes, FIG. 9 illustrates a case where a projection quadrangle isphotographed by a second segment camera which an apparatus forcalibrating a camera according to an embodiment of the present inventionassumes, FIG. 10 illustrates a case where a projection quadrangle isphotographed by a first segment camera and a second segment camera whichan apparatus for calibrating a camera according to an embodiment of thepresent invention assumes, FIG. 11 illustrates geometric relationship ofa projection center line, a centered quadrangle and a projectionquadrangle which are used by an apparatus for calibrating a cameraaccording to an embodiment of the present invention, FIG. 12 illustratesa centered quadrangle which an apparatus for calibrating a cameraaccording to an embodiment of the present invention estimates, FIG. 13illustrates a case where an environment quadrangle is photographed by afirst segment camera which an apparatus for calibrating a cameraaccording to an embodiment of the present invention assumes, and FIG. 14illustrates a projection center point of a segment camera which anapparatus for calibrating a camera according to an embodiment of thepresent invention assumes.

Referring to FIG. 7, when it is assumed that a projection quadrangle(V₀, V₁, V₂, V₃) is a quadrangle having Vm of an intersection point ofdiagonals and f of an angle of diagonals, a process for photographing animage quadrangle through a segment camera pair will be explained below.Here, since the segment camera is a virtual camera to explain operationprinciple of an apparatus for calibrating a camera according to anembodiment of the present invention, the apparatus for calibrating acamera does not perform actual photographing through the segment camera.

It is assumed that the apparatus for calibrating a camera lets twovirtual segment cameras photograph each diagonal of an environmentquadrangle at a projection center point P_(c). Length of a projectioncenter line may be estimated using a diagonal length of the image, whicheach segment camera photographed (that is a diagonal length of acentered quadrangle), and a diagonal length of the environmentquadrangle. Referring to FIG. 8 and FIG. 9, it is assumed that eachsegment camera photographs each diagonal of a projection quadrangle at aprojection center point. That is, a first segment camera may be asegment camera which photographs to form a projection center line to bean angle of θ₀ with one diagonal of the projection quadrangle and asecond segment camera may be a segment camera which photographs to forma projection center line to be an angle of θ₁ with the other diagonal ofthe projection quadrangle.

Referring to FIG. 10, the segments photographed by the first segmentcamera and the second segment camera cross with each other and acentered quadrangle, of which diagonals are the segments, may beprojected and generated as an image as shown in FIG. 11. Thus, when theenvironment quadrangle is photographed, the image including the centeredquadrangle may be generated as shown in FIG. 12.

Here, the apparatus for calibrating a camera may calculate length of theprojection center line (P_(c), V_(m)) based on geometric relationshipbetween the projection quadrangle (V₀, V₁, V₂, V₃) and the centeredquadrangle (U₀, U₁, U₂, U₃).

Referring to FIG. 13, a projection type for the diagonal of theenvironment quadrangle of the first segment camera may be represented bya planar triangle, not three-dimensional triangle. Here, the projectiontype for the diagonal of the environment quadrangle of the secondsegment camera may be also represented by a planar triangle as shown inFIG. 13. When m₀, m₂, l₀, and l₂ are known and all points which can beprojection centers of the first segment camera are represented accordingto the geometric relationship, a sphere having a center point C may beformed as shown in FIG. 14. When a segmentation diagonal ratio of theprojection quadrangle (m₀:m₂) and a segmentation diagonal ratio of thecentered quadrangle (l₀:l₂) are known, a projection center of thesegment camera photographing diagonal of the projection quadrangle maybe a certain point on one sphere. Therefore, any one point, which is aprojection center corresponding to the first segment camera and thesecond segment camera, among intersection cycles which are formed withintersection points of the sphere may be a common projection center ofthe first segment camera and the second segment camera. Here, it isassumed that the segmentation diagonal ratio of the projectionquadrangle is identical to the segmentation diagonal ratio of theenvironment quadrangle. Accordingly, the following Equation 1 may beprovided using each segmentation diagonal ratio of the projectionquadrangle and the centered quadrangle and the length of the projectioncenter line:

$\begin{matrix}{{\cos\;\theta_{i}} = {{\frac{{m_{i + 2}l_{i}} - {m_{i}l_{i + 2}}}{m_{i}{m_{i + 2}\left( {l_{i} + l_{i + 2}} \right)}}d} = {\alpha_{p,i}d}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

wherein m_(i) is a segmentation diagonal ratio to one diagonal of theprojection quadrangle, m_(i+2) is a segmentation diagonal ratio to theother diagonal of the projection quadrangle (Here, i is 0 or 1), l_(i)is the segmentation diagonal ratio for one diagonal of the centeredquadrangle, l_(i+2) is a segmentation diagonal ratio to the otherdiagonal of the centered quadrangle, d is a length of a projectioncenter line. θ₀ is an angle between the diagonal which the first segmentcamera photographs and the projection center line, θ₁ is an anglebetween the diagonal which the second segment camera photographs and theprojection center line.

$\begin{matrix}{\beta = {\frac{l_{1}}{l_{0}} = {\frac{m_{1}\sin\;\theta_{i}}{m_{0}\sin\;\theta_{0}}\frac{\left( {d - {m_{0}\cos\;\theta_{0}}} \right)}{\left( {d - {m_{1}\cos\;\theta_{1}}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

wherein, l₀ is a distance between one end of the diagonal of the imagegenerated through the first segment camera (the segment camera whichphotographs the diagonal (V₀, V₂) of the projection quadrangle) and theintersection point of the diagonals of the centered quadrangle, l₁ is adistance between one end of the diagonal of the image generated throughthe second segment camera (the segment camera which photographs thediagonal (V₁, V₃) of the projection quadrangle) and the intersectionpoint of the diagonals of the centered quadrangle. m₀ is a distancebetween the intersection point of the diagonals of the projectionquadrangle and the diagonal (V₀, V₂) and m₁ is a distance between theintersection point of the diagonals of the projection quadrangle and thediagonal (V₁, V₃).

Equation 3 may be provided by applying the Equation 2 to the Equation 1.

$\begin{matrix}{\mspace{79mu}{{d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}}{{{where}\mspace{14mu} A_{p,0}} = {{{m_{0}^{2}\left( {1 - {m_{1}\alpha_{p,1}}} \right)}^{2}\beta^{2}} - {m_{1}^{2}\left( {1 - {m_{0}\alpha_{p,0}}} \right)}^{2}}}{{{and}\mspace{14mu} A_{p,1}} = {{m_{0}^{2}{\alpha_{p,0}^{2}\left( {1 - {m_{1}\alpha_{p,1}}} \right)}^{2}\beta^{2}} - {{m_{1}^{2}\left( {1 - {m_{0}\alpha_{p,0}}} \right)}^{2}{\alpha_{p,1}^{2}.}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

Accordingly, the apparatus for calibrating a camera may calculate alength of the projection center line using the segmentation diagonalratio of the centered quadrangle and the segmentation diagonal ratio ofthe projection quadrangle.

The apparatus for calibrating a camera may then calculate θ₀ and θ₁which are angles between the diagonal of each segment camera and theprojection center line by applying the length of the projection centerline to the Equation 1.

The apparatus for calibrating a camera may further calculate a diagonalangle of the projection quadrangle by applying θ₀ and θ₁ to thefollowing Equation 4.cos φ=cos ρ sin θ₀ sin θ₁+cos θ₀ sin θ₁  [Equation 4]Here, ρ is a diagonal angle of the centered quadrangle and φ is adiagonal angle of the projection quadrangle.

The apparatus for calibrating a camera may calculate a projection centerpoint (P_(c)) using the following Equation 5.

$\begin{matrix}{P_{c} = \frac{d\left( {{\sin\;\phi\;\cos\;\theta_{0}\cos\;\theta_{1}} - {\cos\;\phi\;\cos\;\theta_{0}\sin\;\rho\;\sin\;\theta_{0}\sin\;\theta_{1}}} \right)}{\sin\;\phi}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Hereinafter, a process for recovering the environment quadrangle usingthe centered quadrangle and the projection quadrangle by the apparatusfor calibrating a camera will be explained below.

FIG. 15 illustrates geometric relationship between an environmentquadrangle and an image quadrangle which an apparatus for calibrating acamera according to an embodiment of the present invention inputs, FIG.16 illustrates a centered quadrangle which an apparatus for calibratinga camera according to an embodiment of the present invention generates,FIG. 17 illustrates geometric relationship between an image quadrangleand an environment quadrangle which an apparatus for calibrating acamera according to an embodiment of the present invention inputs, acentered quadrangle and a projection quadrangle, and FIG. 18 is a planview illustrating an environment quadrangle and a projection quadranglewhich an apparatus for calibrating a camera according to an embodimentof the present invention estimates.

The apparatus for calibrating a camera according to an embodiment of thepresent invention may extract an image quadrangle 1520 from an imagegenerated by photographing an environment quadrangle 1510 as shown inFIG. 15. The apparatus for calibrating a camera may estimate a centeredquadrangle 1530 from the image quadrangle 1520 using vanishing-points asshown in FIG. 16. The apparatus for calibrating a camera may alsoestimate a projection quadrangle 1540 from the centered quadrangle 1530through concept of using a virtual segment camera as shown in FIG. 17.Here, the apparatus for calibrating a camera may estimate a homographybetween the centered quadrangle 1530 and the projection quadrangle 1540.The apparatus for calibrating a camera may recover the environmentquadrangle 1510 by applying the homography to the image quadrangle 1520.As shown in FIG. 18, geometric relationship between the projectionquadrangle 1540, which is a similar figure to the environment quadrangle1510, and the centered quadrangle 1530 is almost similar to that betweenthe environment quadrangle 1510 and the image quadrangle 1520.Therefore, the apparatus for calibrating a camera may recover theenvironment quadrangle 1510 from the image quadrangle 1520 using thehomography between the centered quadrangle 1530 and the projectionquadrangle 1540.

The apparatus for calibrating a camera may be used for image-basedbuilding modeling using a quadrocopter or mobile document scanners.

For example, the apparatus for calibrating a camera according to anembodiment of the present invention may be used for image-based buildingmodeling using a quadrocopter as follows.

Summary Image-based modeling technology for buildings having manyquadrangle elements using a quadrocopter. A quadrocopter equipped with acamera identifies its own position while flying around a building, andobtains dense images of the building through sequential photographingfeatures (e.g., walls, windows and the like). 3D image- based modelingis performed for the building by connecting those pictures. SystemQuadrangle information, mainly rectangular information of constructionthe building is used but length of a segmentation diagonal using anoriginal building plan is used when it available. A camera of which lensdistortion is calibrated. A self-driving or human-driven quadrocopterequipped with a camera Application software and drive server: processesimages when the quadrocopter transmits photographed images, extractsfeatures(quadrangles), controls position of the quadrocopter, plans anext shooting position, and performs image-based modeling by assemblingthe photographed images. Terminal Basically constructed of thequadrocopter and drive software and Photographing a building (or anequivalent rectangular) application and transmitting the image to theserver through WiBro and WiFi communication methods. System Thetransmitted images are analyzed using the method of service the presentinvention and a shooting position of the quadrocopter is obtained. Theimages are assembled and the next shooting position of the quadrocopteris determined and the quadrocopter is moved.

The apparatus for calibrating a camera according to an embodiment of thepresent invention may be used for a mobile document scanner as shown thefollowing Table.

Summary Various rectangular documents (prints, cards, books, etc.) ofwhich aspect ratios are not known are photographed and recovered inrectangular forms of images. It is not necessary to know aspect ratiosof the documents in advance during this process, One image is enough.System A smartphone equipped with a camera construction Core functionsoftware: extracts and processes quadrangle areas from images when auser photographs documents and recovers the images by calculating aspectratios of the rectangulars. Additional Result may be better when lensdistortion of the smartphone functions is calibrated. Quality of theimage may be improved though texture filtering when the identicaldocument is photographed from different angles. The user may activelyset or correct a quadrangle area.

FIG. 19 illustrates the computer system implemented with the apparatusfor calibrating a camera in accordance with an embodiment of the presentinvention.

An embodiment of the present invention may be implemented in a computersystem, e.g., as a computer readable medium. As shown in in FIG. 1900, acomputer system 1920-1 may include one or more of a processor 1921, amemory 1923, a user input device 1926, a user output device 1927, and astorage 1928, each of which communicates through a bus 1922. Thecomputer system 1920-1 may also include a network interface 1929 that iscoupled to a network 1930. The processor 1921 may be a centralprocessing unit (CPU) or a semiconductor device that executes processinginstructions stored in the memory 1923 and/or the storage 1928. Thememory 1923 and the storage 1928 may include various forms of volatileor non-volatile storage media. For example, the memory may include aread-only memory (ROM) 1924 and a random access memory (RAM) 1925.

Accordingly, an embodiment of the invention may be implemented as acomputer implemented method or as a non-transitory computer readablemedium with computer executable instructions stored thereon. In anembodiment, when executed by the processor, the computer readableinstructions may perform a method according to at least one aspect ofthe invention.

The spirit of the present invention has been described by way of examplehereinabove, and the present invention may be variously modified,altered, and substituted by those skilled in the art to which thepresent invention pertains without departing from essential features ofthe present invention. As such, many embodiments other than that setforth above can be found in the appended claims. Accordingly, theexemplary embodiments disclosed in the present invention and theaccompanying drawings do not limit but describe the spirit of thepresent invention, and the scope of the present invention is not limitedby the exemplary embodiments and accompanying drawings. The scope of thepresent invention should be interpreted by the following claims and itshould be interpreted that all spirits equivalent to the followingclaims fall within the scope of the present invention.

What is claimed is:
 1. An apparatus for calibrating a camera comprising:a camera configured to generate an image quadrangle in an image byphotographing an environment quadrangle; an input unit configured toreceive a segmentation diagonal ratio of the environment quadrangle; aprocessor; a non-transitory computer-readable medium whose contents,when executed by the processor, cause the processor to perform cameracalibration operations, the camera calibration operations comprising:generating a centered quadrangle using first and second vanishing lines,the first and second vanishing lines connecting a center of the image toa pair of vanishing points; extracting diagonal parameters of thecentered quadrangle from the image estimating a length of a projectioncenter line based on the segmentation diagonal ratio of the environmentquadrangle and the diagonal parameters of the centered quadrangle;estimating a projection angle corresponding to each diagonal of thecentered quadrangle based on the length of the projection center line;estimating an angle between diagonals of a projection quadrangle basedon the projection angle and an angle between diagonals of the centeredquadrangle; estimating a projection center point based on the projectionangle, the angle between diagonals of the centered quadrangle and theangle between diagonals of the projection quadrangle; and estimatingextrinsic and intrinsic parameters of the camera corresponding to theprojection center point and the centered quadrangle, wherein thecentered quadrangle is generated by: detecting first extensionintersection points, the first extension intersection points beingintersections of extension lines of each side of the image quadrangleand a segment connecting two vanishing points; detecting secondextension intersection points, the second extension intersection pointsbeing intersections of the vanishing lines and one of the extensionlines; and detecting third extension intersection points, the thirdextension intersection points being intersections of the centeredvanishing lines and lines connecting the first and second extensionintersection points, and wherein the second and third extensionintersection points are vertices of the centered quadrangle.
 2. Theapparatus for calibrating a camera of claim 1, wherein the diagonalparameter comprises the angle between diagonals of the centeredquadrangle and the segmentation diagonal ratio.
 3. The apparatus forcalibrating a camera of claim 1, wherein the projection angle is anangle between the projection center line and the diagonal of theenvironment quadrangle.
 4. The apparatus for calibrating a camera ofclaim 1, wherein the camera calibration operations further comprise:estimating a homography between the centered quadrangle and theprojection quadrangle; and recovering the environment quadrangle byapplying the homography to the image quadrangle.
 5. The apparatus forcalibrating a camera of claim 1, wherein the length of the projectioncenter line is estimated by the following Equation:$d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}$where  A_(p, 0) = m₀²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²and  A_(p, 1) = m₀²α_(p, 0)²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²α_(p, 1)².wherein the m₀ is a segmentation diagonal ratio to one diagonal of theprojection quadrangle, the m₁ is a segmentation diagonal ratio to theother diagonal of the projection quadrangle, and β is a value obtainedby dividing the segmentation diagonal ratio to one diagonal of thecentered quadrangle by the segmentation diagonal ratio to the otherdiagonal of the centered quadrangle.
 6. The apparatus for calibrating acamera of claim 1, wherein the projection angle is estimated by thefollowing Equation:${\cos\;\theta_{i}} = {{\frac{{m_{i + 2}l_{i}} - {m_{i}l_{i + 2}}}{m_{i}{m_{i + 2}\left( {l_{i} + l_{i + 2}} \right)}}d} = {\alpha_{p,i}d}}$wherein the m_(i) is a segmentation diagonal ratio to one diagonal ofthe projection quadrangle, the m_(i)+2 is a segmentation diagonal ratioto the other diagonal of the projection quadrangle, the l_(i) is asegmentation diagonal ratio to one diagonal of the centered quadrangle,the l_(i)÷2 is a segmentation diagonal ratio to the other diagonal ofthe centered quadrangle, d is length of the projection center line, theθ_(i) is a projection angle corresponding to each diagonal of thecentered quadrangle, the i is 0 or
 1. 7. The apparatus for calibrating acamera of claim 1, wherein the angle between the diagonals is estimatedby the following Equation:cos φ=cos ρ sin θ₀ sin θ₁ +cos θ₀ sin θ₁ wherein the ρ is an anglebetween the diagonals of the centered quadrangle, the φ is an anglebetween diagonals of the projection quadrangle, the θ₀ is a projectionangle corresponding to one diagonal of the centered quadrangle, θ₁ is aprojection angle corresponding to the other diagonal of the centeredquadrangle.
 8. The apparatus for calibrating a camera of claim 1,wherein the projection center point is estimated by the followingEquation:$P_{c} = \frac{d\left( {{\sin\;\phi\;\cos\;\theta_{0}\cos\;\theta_{1}} - {\cos\;\phi\;\cos\;\theta_{0}\sin\;\rho\;\sin\;\theta_{0}\sin\;\theta_{1}}} \right)}{\sin\;\phi}$wherein P_(c) is a projection center point, the ρ is an angle betweenthe diagonals of the centered quadrangle, the φ is an angle betweendiagonals of the projection quadrangle, the θ₀ is a projection anglecorresponding to one diagonal of the centered quadrangle, θ₁is aprojection angle corresponding to the other diagonal of the centeredquadrangle, d is length of the projection center line.
 9. A method forcalibrating a camera in which an apparatus for calibrating a cameraperforms camera calibration, the method comprising: receiving an imagequadrangle of an environment quadrangle in an image and a segmentationdiagonal ratio of the environment quadrangle; generating a centeredquadrangle using first and second vanishing lines, the first and secondvanishing lines connecting a center of the image to a pair of vanishingpoints; extracting diagonal parameters of the centered quadrangle fromthe image; estimating length of a projection center line based on thesegmentation diagonal ratio of the environment quadrangle and thediagonal parameters of the centered quadrangle; estimating a projectionangle corresponding to each diagonal of the centered quadrangle based onthe length of the projection center line; estimating an angle betweendiagonals of a projection quadrangle based on the projection angle andan angle between diagonals of the centered quadrangle; estimating aprojection center point based on the projection angle, the angle betweendiagonals of the centered quadrangle and the angle between diagonals ofthe projection quadrangle; and estimating extrinsic and intrinsicparameters of the camera corresponding to the projection center pointand the centered quadrangle, wherein the centered quadrangle isgenerated by: detecting first extension intersection points, the firstextension intersection points being intersections of extension lines ofeach side of the image quadrangle and a segment connecting two vanishingpoints; detecting second extension intersection points, the secondextension intersection points being intersections of the vanishing linesand one of the extension lines; and detecting third extensionintersection points, the third extension intersection points beingintersections of the centered vanishing lines and lines connecting thefirst and second extension intersection points, and wherein the secondand third extension intersection points are vertices of the centeredquadrangle.
 10. The method for calibrating a camera of claim 9, whereinthe diagonal parameter comprises the angle between diagonals of thecentered quadrangle and the segmentation diagonal ratio.
 11. The methodfor calibrating a camera of claim 9, wherein the projection angle is anangle between the projection center line and the diagonal of theenvironment quadrangle.
 12. The method for calibrating a camera of claim9, further comprising: estimating a homography between the centeredquadrangle and the projection quadrangle; and recovering the environmentquadrangle by applying the homography to the image quadrangle.
 13. Themethod for calibrating a camera of claim 9, wherein the step forestimating length of a projection center line based on the segmentationdiagonal ratio of the environment quadrangle and the diagonal parametersof the centered quadrangle comprises estimating length of a projectioncenter line by the following Equation:$d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}$where  A_(p, 0) = m₀²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²and  A_(p, 1) = m₀²α_(p, 0)²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²α_(p, 1)².wherein the m₀ is a segmentation diagonal ratio to one diagonal of theprojection quadrangle, the m₁ is a segmentation diagonal ratio to theother diagonal of the projection quadrangle, β is a value obtained bydividing the segmentation diagonal ratio to one diagonal of the centeredquadrangle by the segmentation diagonal ratio to the other diagonal ofthe centered quadrangle.
 14. The method for calibrating a camera ofclaim 9, wherein the step for estimating a projection anglecorresponding to each diagonal of the centered quadrangle based on thelength of the projection center line comprises estimating a projectionangle by the following Equation:${\cos\;\theta_{i}} = {{\frac{{m_{i + 2}l_{i}} - {m_{i}l_{i + 2}}}{m_{i}{m_{i + 2}\left( {l_{i} + l_{i + 2}} \right)}}d} = {\alpha_{p,i}d}}$wherein the m_(i) is a segmentation diagonal ratio to one diagonal ofthe projection quadrangle, the m_(i)+2 is a segmentation diagonal ratioto the other diagonal of the projection quadrangle, the l_(i) is asegmentation diagonal ratio to one diagonal of the centered quadrangle,the l_(i)+2 is a segmentation diagonal ratio to the other diagonal ofthe centered quadrangle, d is length of the projection center line, theθ_(i) is a projection angle corresponding to each diagonal of thecentered quadrangle, the i is 0 or
 1. 15. The method for calibrating acamera of claim 9, wherein the step for estimating an angle betweendiagonals of a projection quadrangle based on the projection angle andan angle between diagonals of the centered quadrangle comprisesestimating an angle between diagonals by the following Equation:cos φ=cos ρ sin θ₀ sin θ₁ +cos θ₀ sin θ₁ wherein the ρ is an anglebetween the diagonals of the centered quadrangle, the φ is an anglebetween diagonals of the projection quadrangle, the θ₀ is a projectionangle corresponding to one diagonal of the centered quadrangle, θ₁ is aprojection angle corresponding to the other diagonal of the centeredquadrangle.
 16. The method for calibrating a camera of claim 9, whereinthe step for estimating a projection center point based on theprojection angle, the angle between diagonals of the centered quadrangleand the angle between diagonals of the projection quadrangle comprisesestimating a projection center point by the following Equation:$P_{c} = \frac{d\left( {{\sin\;\phi\;\cos\;\theta_{0}\cos\;\theta_{1}} - {\cos\;\phi\;\cos\;\theta_{0}\sin\;\rho\;\sin\;\theta_{0}\sin\;\theta_{1}}} \right)}{\sin\;\phi}$wherein P_(c) is a projection center point, the ρ is an angle betweenthe diagonals of the centered quadrangle, the φ is an angle betweendiagonals of the projection quadrangle, the θ₀ is a projection anglecorresponding to one diagonal of the centered quadrangle, θ₁ is aprojection angle corresponding to the other diagonal of the centeredquadrangle, d is length of the projection center line.
 17. A method forcalibrating a camera in which an apparatus for calibrating a cameraperforms camera calibration, the method comprising: receiving an imageof an environment quadrangle and a segmentation diagonal ratio of theenvironment quadrangle; extracting diagonal parameters of a centeredquadrangle from the image; estimating length of a projection center linebased on the segmentation diagonal ratio of the environment quadrangleand the diagonal parameters of the centered quadrangle; estimating aprojection angle corresponding to each diagonal of the centeredquadrangle based on the length of the projection center line; estimatingan angle between diagonals of a projection quadrangle based on theprojection angle and an angle between diagonals of the centeredquadrangle; estimating a projection center point based on the projectionangle, the angle between diagonals of the centered quadrangle and theangle between diagonals of the projection quadrangle; and estimatingextrinsic and intrinsic parameters of the camera corresponding to theprojection center point and the centered quadrangle, wherein the stepfor estimating length of a projection center line based on thesegmentation diagonal ratio of the environment quadrangle and thediagonal parameters of the centered quadrangle comprises estimatinglength of a projection center line by the following Equation:$d = \sqrt{\frac{A_{p,0}}{A_{p,1}}}$where  A_(p, 0) = m₀²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²and  A_(p, 1) = m₀²α_(p, 0)²(1 − m₁α_(p, 1))²β² − m₁²(1 − m₀α_(p, 0))²α_(p, 1)².wherein the m₀ is a segmentation diagonal ratio to one diagonal of theprojection quadrangle, the m₁ is a segmentation diagonal ratio to theother diagonal of the projection quadrangle, β is a value obtained bydividing the segmentation diagonal ratio to one diagonal of the centeredquadrangle by the segmentation diagonal ratio to the other diagonal ofthe centered quadrangle.
 18. The method for calibrating a camera ofclaim 17, further comprising: estimating a homography between thecentered quadrangle and the projection quadrangle; and recovering theenvironment quadrangle by applying the homography to the imagequadrangle.